Static Accelerometer Orientation Tumble Calibration Procedures
Static tumble calibration calculates accelerometer bias, scale factor, and cross-axis matrices by optimizing spatial vector residuals against local gravity.
Levenberg-Marquardt Algorithm
Optimization Routine
Iterative numerical optimization methods solve multi-dimensional regression problems by blending gradient descent and Gauss-Newton update steps. In sensor calibration, the Levenberg-Marquardt algorithm is applied to find the sensor biases and scale factors that minimize the residuals of the measurements. This method operates on a set of calibration data collected during multi-axis rotation tests.
The routine halts when the change in the cost function falls below a predefined threshold.
Damping Adjustment
An adjustable damping parameter controls the transition between the two optimization strategies during the execution. If the Levenberg-Marquardt algorithm faces a highly non-linear region, the damping value increases to favor the gradient descent approach. Conversely, as the solution nears the optimal values, the damping is reduced to exploit the faster convergence of the Gauss-Newton method.
This adaptability ensures stability even when the initial parameter estimates are far from the true values.
Calibration Convergence
Achieving a stable and accurate parameter set depends on the formulation of the jacobian matrix and the quality of the sensor dataset. When executing the Levenberg-Marquardt algorithm, poor sensor excitation can lead to a singular jacobian matrix, causing the algorithm to stall in a local minimum. To prevent this, the calibration trial must include diverse angular positions that exercise all the axis combinations.
The convergence speed is monitored by tracking the norm of the gradient at each step. If the gradient does not decrease, the input dataset is flagged as insufficient.
Numerical Computation
High computational efficiency makes this optimization method suitable for automated calibration software running on production lines. Since the Levenberg-Marquardt algorithm requires matrix inversion, the dimension of the parameter vector is kept small to avoid high processing delays. Standard sensor modules with nine parameters can be calibrated in a few milliseconds on a typical microprocessor.